A Flexible Global GCRO-DR Method for Shifted Linear Systems and General Coupled Matrix Equations
In this paper, we mainly focus on the development and study of a new global GCRO-DR method that allows both the flexible preconditioning and the subspace recycling for sequences of shifted linear systems. The novel method presented here has two main advantages: firstly, it does not require the right...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5589582 |
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| author | Jing Meng Xian-Ming Gu Wei-Hua Luo Liang Fang |
| author_facet | Jing Meng Xian-Ming Gu Wei-Hua Luo Liang Fang |
| author_sort | Jing Meng |
| collection | DOAJ |
| description | In this paper, we mainly focus on the development and study of a new global GCRO-DR method that allows both the flexible preconditioning and the subspace recycling for sequences of shifted linear systems. The novel method presented here has two main advantages: firstly, it does not require the right-hand sides to be related, and, secondly, it can also be compatible with the general preconditioning. Meanwhile, we apply the new algorithm to solve the general coupled matrix equations. Moreover, by performing an error analysis, we deduce that a much looser tolerance can be applied to save computation by limiting the flexible preconditioned work without sacrificing the closeness of the computed and the true residuals. Finally, numerical experiments demonstrate that the proposed method illustrated can be more competitive than some other global GMRES-type methods. |
| format | Article |
| id | doaj-art-b30fc6f1f5c54e8898bb5bbce0d6e6af |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-b30fc6f1f5c54e8898bb5bbce0d6e6af2025-08-20T03:39:18ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55895825589582A Flexible Global GCRO-DR Method for Shifted Linear Systems and General Coupled Matrix EquationsJing Meng0Xian-Ming Gu1Wei-Hua Luo2Liang Fang3School of Mathematics and Statistics, Taishan University, Taian 271021, Shandong, ChinaInstitute of Mathematics, School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, ChinaSchool of Mathematics and Physics Science, Hunan University of Arts and Science, Changde, Hunan 415000, ChinaSchool of Mathematics and Statistics, Taishan University, Taian 271021, Shandong, ChinaIn this paper, we mainly focus on the development and study of a new global GCRO-DR method that allows both the flexible preconditioning and the subspace recycling for sequences of shifted linear systems. The novel method presented here has two main advantages: firstly, it does not require the right-hand sides to be related, and, secondly, it can also be compatible with the general preconditioning. Meanwhile, we apply the new algorithm to solve the general coupled matrix equations. Moreover, by performing an error analysis, we deduce that a much looser tolerance can be applied to save computation by limiting the flexible preconditioned work without sacrificing the closeness of the computed and the true residuals. Finally, numerical experiments demonstrate that the proposed method illustrated can be more competitive than some other global GMRES-type methods.http://dx.doi.org/10.1155/2021/5589582 |
| spellingShingle | Jing Meng Xian-Ming Gu Wei-Hua Luo Liang Fang A Flexible Global GCRO-DR Method for Shifted Linear Systems and General Coupled Matrix Equations Journal of Mathematics |
| title | A Flexible Global GCRO-DR Method for Shifted Linear Systems and General Coupled Matrix Equations |
| title_full | A Flexible Global GCRO-DR Method for Shifted Linear Systems and General Coupled Matrix Equations |
| title_fullStr | A Flexible Global GCRO-DR Method for Shifted Linear Systems and General Coupled Matrix Equations |
| title_full_unstemmed | A Flexible Global GCRO-DR Method for Shifted Linear Systems and General Coupled Matrix Equations |
| title_short | A Flexible Global GCRO-DR Method for Shifted Linear Systems and General Coupled Matrix Equations |
| title_sort | flexible global gcro dr method for shifted linear systems and general coupled matrix equations |
| url | http://dx.doi.org/10.1155/2021/5589582 |
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